Vector calculating board



Nov. 3, 1942- D. E. BASLER arm. 2,300,401

VECTOR CALCULATING BOARD Filed Aug. 30, 1941 Bi ycle F290 20 L9 /23 Z0'4.

WVIIIIIIVVAIFIIIIA HAROLD VIZ/KELL Y BEL/650mm [NVENTORS fibf? WATTORNEY Patented, Nov. 3, 1942' UNITED STATES PATENT OFFICE" z,s 6o,4o1

VECTOR CALCULATING BOARD pom a Ba'sler, 1m... Mlcla, Harold w. Kelley,Port St Joe, Fla, and Bruce 0. Watkins,

Tucson, Aria.

(Granted under the act of March s, 188:, amended April so, 1928; m o. G.751;

Claims.

The invention described herein may be manufactured and used by or forthe Government of the United States for governmental purposes withoutthe payment to us of any royalty thereon in accordance with theprovisions of the act of April 30, 1928 (Ch. 460, 45 Stat. L. 467) Thisinvention relates to a mechanical calties or vectors such as impedances,displacements,

velocities, forces, etc. (all of which are quantities involving the ideaof direction as well as amount) must be dealt with in the treatment ofmany problems. Problems involving addition and subtraction .of vectorsmay be solved either mathematically or graphically. The instantinvention relates to devices for readily solving such problems bygraphic methods without thenecessity of laborlus computation.

An object of this invention is to provide a mechanism havingintersecting elongated members movable with respect to suitablecoordinate scales, together with a graduated elongated member pivoted atthe point of origin of or the effective intersection of said scalestogether with means for maintaining the swinging portion of saidgraduated pivoted member above the point of'intersection of saidelongated members and a protractor scale associated with said graduatedmember whereby the distance between the point of origin of said scalesand the point of intersection of said movable members may be read on thepivoted graduated member while the direction of having a flat topsurface and parallel opposite edges resembling a rectangular drawingboard. An elongated straight edge member I rests on the base I. A secondelongated straight edge member 3 rests on the base I atop the straightedge member {and perpendicular to it. The straight edge members 2 and 3are provided with 1' square ends engaging the respective edges of thebase i so that each straightedge member is capable of sliding movementto and fro over the base along one axis. (It is to be understood howeverthat straight edge members 2 and 3 may be movably mounted with respectto the base I in a manner similar to the mounting of the straightcoordinate members shown in United Statespatent to Trueblood et al. No.1,440,510 or United States patent to Webster No. 1,442,710.)

A third straight edge member 4 is pivotally mounted on pin 5 carried bythe bracket 6 mounted on the base i. The, straight edge member 3overlies the straight edge members 2 and 3. The pivot pin 5 is sopositioned that the straight edge member I pivots about the zero-zeropoint on the coordinate scales 1 and 8 engraved or otherwise marked uponthe base I. Adjacent to the ordinate scales 1 the base I is providedwith grooved slots Ill carrying additional scales 9. Adjacent to theabscissa scales 3 the base is provided with grooved slots l2 carryingadditional scales ii. The base i is also provided with two pairs 0!narrow parallel slots. The slots I are parallel to the ordinate scalesand the slots ii are parallel to the abscissa scales. The slots l3 andI! are provided for the purpose of receiving the spring ends of U-shapedindex tabs designated I3 and i5, respectively. The straight edge members2, 3 and 4; while they may be made of wood, metal or the like, are shownas being made of transparent plastic. The members land 3 are providedwith hair line index markings I1 and I8, respectively, engraved thereonfor association with the respective coordinate scales 1 and 8 on base I.Encompassing the point of crossing of straight edges 2, 3 and 4 there islocated a slide member l9 (Figure 2). This member includes a straightedge holding portion 20 provided with an aperture therethrough of suchsize as to snugly receive the straight edge member 4. The slide memberI! also includes second and third straight edge holding portions 2| and22 having apertures therethrough of such a size as to snugly receive thestraight edge members 3 and 2, respectively.- The last mentionedportions are made integral and the apertures therein are at right anglesto each other with the straight edge members 3 and 2 passing throughtheir respective apertures. The straight edge holding portion 20 of theslide member I! is pivotally fastened to the lower portion of thismember by the pivot bolt or pin 23. -The straight edge holding portion20 of the slide member may be made of metal or transparent plastic. Inthe illustrated embodiment it is shown as being made of metal with arectangular portion cut out as viewed in Figure 1, with a cross hair 34stretched thereover perpendicular to the straight edge member 4 carriedthereby. When this member is made of transparent plastic or is providedwith a transparent top of plastic or glass, a line taking the place ofthe cross hair 24 can be engraved or etched directly upon its topwithout the necessity of cutting out material to make the graduations onthe straight edge member 4 visible. The pivoted straight edge member 4is provided with one or more sets of graduations thereon correspondingto the coordinate scales to be used. The member 4 is also provided witha hair line marking longitudinally thereof. The line established by thismarking passes through the pivot axes of the pivot pins 6 and 24. Thepivot axes of the pins and 29 are both normal to the plane of the upperface of the base I and the pivotal axis 22 passes through the point ofintersection of the lines established by the hair line marks I1, 24, andIS. The top of the base I may be ruled to resemble polar coordinategraph paper with the pivotal axis of the pin 5 as the origin, or theserulings may be omitted, but in any event the top of the base I ispreferably provided with the an gular graduations thereon, as shownschematically by the scale 25.

In operation the straight edge members 2 and I are moved with respect totheir coordinate scales, thus moving the slide member IS in accordancewith the resultant compound motion imparted thereto. As the slide memberI9 is moved, the straight edge member 4 is moved thereby, pivoting aboutthe fixed axis of the pivot pin 25. The device can also be operated bymoving the slide member l9 to cause its cross hair 24 to overlie aselected graduation thereon and a desired angular setting of thestraight edge member 4 may be made with respect to the angulargraduations 25, in which case the straight edge members 2 and 3 will bemoved to resolve the vector quantity represented by the distance readofl on the scale carried by the straight edge member 4 and its directioninto two components at right angles to each other.

It will be apparent from the above description that when either thescales 1 and 8 or other suitable scales are employed, this equipment maybe used to perform vectorial addition, subtraction and many other alliedproblems. One example will be given illustrating the use of theequipment for the adding of vectors. In this example it will be assumedthat it is desired to determine the impedance of an electrical circuithaving three ohms of inductive resistance at a particular frequency andhaving four ohms of ohmic resistance. Here the magnitudes of thecomponents are different and their directions differ by ninety degrees.Vectorial addition of these two components is established by moving thestraight edge member 2 to bring its hair line mark il above the, scale Ito the numerical value 9 and then moving the straight edge member I tobring its hair line mark i9 over the scale 8 to the numerical value 4.With the movement of the straight edge members 2 and 3 the slide memberI 9 is moved so that its cross hair 24 lies directly over the numericalindication 5 on the scale carried by straight edge member 4 and theangular displacement of this quantity with respect to either theresistance or the inductance can be read on the scale 25. Where forinstance it is desired to resolve a vector having a magnitude of 183plus and a direction of forty-five degrees with respect to thehorizontal and vertical axes, the straight edge member 4 may beresistance or reactance values.

moved to bring its hair line over ,the graduation of scale 24 and thenthe slide l9 can be slid therealong to indicate the magnitude of thisvector, whereupon the slide members 2 and 3 are moved to bring theirrespective hair lines I! and II to overlie the values and 130 oncoordinate scales 1 and 8, respectively, thus resolving the vector of agiven magnitude and direction into two components at right angles toeach other. I

In the above description simple numerical values have been assumed forthe purpose oi simplicity. It is to be understood that the scales shownon the instrument are not necessarily as accurately laid out orproportioned as the scale graduations in an actual instrument. For thesolution of a great number of problems of this type the additionalscales 9 and II could be graduated to represent ohms, amperes, volts orsome other quantity. In impedance problems scales 8 or II wouldrepresent resistance values in ohms and scales 1 and 9 would representreactance values. The total impedance therefore is read on the scalecarried by the straight edge member 4. For voltage or current, scales 8and H would represent real values while scales I and 9 would representimaginary values. The magnitude of the resultant vector would be read onthe scale carried by straight edge member 4 and the angular displacementby reading the angle between this member and the horizontal. Certain ofthe removable or interchangeable scales 9 and II could be graduated inother manners. For example, a certain size of conductor has a certainresistance and reactance per mile. Therefore, one of the scales of theset ll could he graduated in miles for No. 4 conductor size resistance-Another could be graduated in miles of N0. 6 wire, etc. Similarly, thescales 9 could be graduated in miles for conductor reactance. Then thetotal impedance could be found on straight edge scale 4 by simplyapplying the proper miles of the conductor on scales 9 and II, withoutreferring to either the By the use of the tabs l3 and I5 this processcan be conducted along the line if the conductor size changed, byplacing the index of the proper conductor scale to the previous value ofthe preceding conductor at the distance where the change in conductorsize occurs.

In lieu of the slide mechanism IS the coordinate arms or straight edgemembers 2 and 3 and the pivoted straight edge member 4 could bemaintained in proper relation by making these members slotted and byhaving a pin extend through all three. The device shown in the drawingis limited to a single quadrant, but it is to be distinctly understoodthat the idea could be carried forward where desired to include two ormore quadrants, thus making possible the more ready handling of negativequantities. Other and further modifications could be made withoutdeparting from the spirit of this invention.

What we claim is:

1. A device for mechanically producing the addition and subtraction ofvectors comprising a base, a pair of mutually perpendicular straightedge members mounted on said base and arranged for independent movementthereon in paths perpendicular to their respective longitudinal axes, aplurality of individually slidable difierently calibrated coordinatescales mounted on said base associated with respective ones of saidstraight edge members, a graduated straight edge member, means forpivoting one end of said graduated straight edge member at the effectiveorigin of said coordinate scales, and means carried by the first twomentioned straight edge members for maintaining the graduated straightedge member in such a position as to always overlie the intersection ofsaid members, whereby vectors in quadrature may be added or subtracted.

2. A device in accordance with claim 1, including index marker tabs andmeans for holding said tabs in predetermined selected locations withrespect to said individually slidable differently calibrated coordinatescales whereby said scales may be readily set opposite said tabs toattain certain predetermined selected positions.

3. A calculating device comprising a frame having indicia thereon,members slidable on said frame and crossing each other at right anglesto form opposed rectangles of lesser size than said frame, a pluralityof individually slidable differently calibrated coordinate scalesmounted on said frame associated with respective ones of said members, adivider pivotally mounted on said frame, means for moving said dividerto intersect the point of crossing of said slidable members, at leastone scale carried by said divider, and a protractor scale on said base,

whereby the length and direction of a line extending between the pivotof said pivotally mounted divider and the point of intersection of saidslidable members may be readily ascertained.

4. A device of the class described comprising a rectangular frame havinga plurality of separately adjustable coordinate scales mounted on two ofthe adjacent sides thereof, a pair of elongated adjustable membersmounted on said frame crossing each other at right angles, said membersbeing movable with respect to the coordinate scales along the respectiveedges of said member, a graduated pivoted member pivoting at theeffective intersection of said coordinate scales, and means formaintaining said graduated pivoted member above the intersection of saidmovable members.

5. A device in accordance with claim 4, including tabs for locatingreference points on said coordinate scales, said tabs having means forholding them in predetermined selected positions on said frame wherebysaid separately adjustable scales may be readily set with respect tosaid predetermined selected positions occupied.

by said tabs.

DONNAN E. BASLER, HAROLD W. KELLEY. BRUCE O. WATKINS.

